Spectral Numerical Methods for Solving Uryshon Integral Equations with Non-smooth Kernels
摘要
In the present paper, polynomially based Kantorovich method is proposed to solve nonlinear Uryshon integral equation with a Green’s function type kernel. The projection is chosen to be either the orthogonal projection or an interpolatory projection using Legendre polynomial bases. Using sufficiently accurate numerical quadrature rule, we obtain optimal convergence rates for both approximated and iterated solutions. Some numerical examples are given to show the efficiency of the method.